Natsume from Natsume yuujinchou? I know that's not the saddest childhood ever, but his life seems a bit... realistic, even though it involves yokai. Some other anime characters' pasts are too... unrealistic for me to sympathies with. And the way Natsume got used to his life is kinda sad. And even now, it did mention that it made him sad that he parted with youkai that he got attached to but can never see again. And even as a kid, he didn't have neither human nor youkai friends.

Asuka from Evangelion, natch. You want to punch her in the face for being such a bitch, yet at the same time you want to give her a hug because of her tragic past...

Spoiler Alert! Click to show or hide

Her mom developed Unit 02, and in a contact experiment, the maternal part of her soul was sucked out, so she was commited to a mental hospital, where she ignored Asuka entirely and focused all of her love and affection on a doll. On the day Asuka became a pilot, her mom hanged herself and the doll. Her dad never really cared, and had an affair with the head nurse, Asuka could even hear them doing you-know-what in the next room. This left Asuka with the belief that anyone she openly cared about would leave her, which is the reason why she's such a bitch to Shinji and all.